Layered Reeb graphs for three-dimensional manifolds in boundary representation

Strodthoff, B.; Jüttler, Bert

doi:10.1016/j.cag.2014.09.026

Cited by 8 publications

(3 citation statements)

References 41 publications

(43 reference statements)

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“…The segmentation process has been investigated and explored in several situations. From isogeometric point of view, the segmentation pipeline has been studied for simply connected solids without non-convex edges in [3,4], and for general three-dimensional solids, segmented into simply connected ones in [5].…”

Section: State Of the Artmentioning

confidence: 99%

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THB-splines multi-patch parameterization for multiply-connected planar domains via Template Segmentation

Falini

Jüttler

2019

Journal of Computational and Applied Mathematics

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Section: State Of the Artmentioning

confidence: 99%

“…Then, we can express the solution h of (3) through the representation formula (5), in terms of Dirichlet data…”

Section: Bie For the Laplace Problemmentioning

confidence: 99%

THB-splines multi-patch parameterization for multiply-connected planar domains via Template Segmentation

Falini

Jüttler

2019

Journal of Computational and Applied Mathematics

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“…However, current research shows that the Jacobi Sets are unable to capture the actual topological changes of multi-fields, instead one should consider their Reeb Spaces, introduced in [19]. Recently, Multi-Dimensional Reeb Graphs [10] and Layered Reeb Graphs [51] have been introduced from two different perspectives to extend the Reeb Graph for multi-fields. In the current paper, we use the recently introduced Jacobi Structure [10] to separate the Reeb Space into regular and singular components.…”

Section: Multi-field Simplificationmentioning

confidence: 99%

Multivariate topology simplification

Chattopadhyay

Carr

Duke

et al. 2016

Computational Geometry

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Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on "lip"-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph.

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Isogeometric Analysis: Representation of Geometry

Haberleitner

Jüttler

Scott

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This chapter provides a review of analysis‐suitable geometric descriptions and approaches commonly used in the context of isogeometric analysis (IGA). A primary focus is on NURBS (nonuniform rational B‐splines), T‐splines, and hierarchical B‐splines. The integration of analysis‐suitable geometry and IGA using Bézier extraction is covered, as well as several emerging approaches to isogeometric mesh generation, adaptivity, and domain parameterization.

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Layered Reeb graphs for three-dimensional manifolds in boundary representation

Cited by 8 publications

References 41 publications

THB-splines multi-patch parameterization for multiply-connected planar domains via Template Segmentation

THB-splines multi-patch parameterization for multiply-connected planar domains via Template Segmentation

Multivariate topology simplification

Isogeometric Analysis: Representation of Geometry

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